They left in the early hours of Tuesday from the bus terminal in the crime-ridden Honduran city of San Pedro Sula.
More are expected to set off later on Tuesday.
It comes as thousands of Hondurans and other Central Americans remain stranded in Tijuana on the US-Mexico border after they walked for thousands of miles as part of a caravan in October.
US President Donald Trump, who railed against the earlier caravan ahead of the US midterm elections, tweeted on Tuesday that the migrants could only be stopped by a "wall or steel barrier" of the type he has been proposing be built on the US-Mexico border.
BBC News Online's Latin America editor Vanessa Buschschlüter travelled to San Pedro Sula and nearby towns to speak to some of those who were leaving and found that while many want to reach the US, some are also heading to Mexico.
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